### SignalProcessing.Compute.Filter.Convolve

This node computes the convolution $\mathrm{c}[n]$ of two signals $\mathrm{a}[n]$ and $\mathrm{b}[n]$:

$\mathrm{c}[n] = \sum\limits_{k = -\infty}^{\infty} \mathrm{a}[k] \, \,\mathrm{b}[n-k]$

For all $k$ for which the signals $\mathrm{a}[k]$ and $\mathrm{b}[n-k]$ are not defined, the signal values are set to zero.

The length of the resulting signal is: $\text{length}(\mathrm{c}) = \text{length}(\mathrm{a})+ \text{length}(\mathrm{b})-1$.

#### Example

$\mathrm{a}[k]$
$\mathrm{b}[k]$
$\mathrm{c}[n]$

In order to get a better understanding of the convolution, the diagrams below visualize the construction of $c[n]$ for four selected $n$, namely $c[0]$, $c[1]$, $c[5]$, and $c[7]$. The signal $\mathrm{b}[n-k]$ can be constructed from $\mathrm{b}[k]$ by a flip around the vertical axis and a shift to the right by $n$. Therefore, for increasing $n$ the signal $\mathrm{b}[n-k]$ slides from left to right over $\mathrm{a}[k]$. The yellow squares below mark those signal values that are involved in the computation of $c[n]$ for a selected $n$:

$\mathrm{a}[k]$
$\mathrm{b}[0-k]$
$\mathrm{a}[k]$
$\mathrm{b}[1-k]$
$\mathrm{c}[0]$
$\mathrm{c}[n]$
$\mathrm{c}[1]$
$\mathrm{c}[n]$
$\mathrm{b}[5-k]$
$\mathrm{b}[7-k]$
$\mathrm{c}[5]$
$\mathrm{c}[7]$